{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FXVEAK6I4SB2RR32NBJ7IOJNUU","short_pith_number":"pith:FXVEAK6I","canonical_record":{"source":{"id":"1207.0337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T10:49:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c7c62628d78aecea939a236364e91e8b607217fc711b108ff9c1d396aa085106","abstract_canon_sha256":"e7dbfcb9167253a00f3513d0190a0074726811e2162cf39329542c7b3b545125"},"schema_version":"1.0"},"canonical_sha256":"2dea402bc8e483a8c77a6853f4392da508679e11ae40ae3ec3c894dc1b2063b0","source":{"kind":"arxiv","id":"1207.0337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0337","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0337v1","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0337","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"FXVEAK6I4SB2","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FXVEAK6I4SB2RR32","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FXVEAK6I","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FXVEAK6I4SB2RR32NBJ7IOJNUU","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T10:49:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c7c62628d78aecea939a236364e91e8b607217fc711b108ff9c1d396aa085106","abstract_canon_sha256":"e7dbfcb9167253a00f3513d0190a0074726811e2162cf39329542c7b3b545125"},"schema_version":"1.0"},"canonical_sha256":"2dea402bc8e483a8c77a6853f4392da508679e11ae40ae3ec3c894dc1b2063b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:59.581844Z","signature_b64":"M9ZL8RaZAxRjgECl+pUC9RwP2JuiF2/SWElG0RYGEdczwiFS+61QAykjbuF8ZCNQQ2MySxSyOuToPic8OpIcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dea402bc8e483a8c77a6853f4392da508679e11ae40ae3ec3c894dc1b2063b0","last_reissued_at":"2026-05-18T03:51:59.581328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:59.581328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0337","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6rsqlZ6dWnj2Zv7mkf37iHdYCK3YfDXZDc6kSCZWwgcir51+AI0Q6WPXmA1rx6TlaW2cRt+a8HsqpA9AKvzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:54:04.752787Z"},"content_sha256":"98c8ff244fe048d44b271c61dae7c7d35d4b3fa061599e25a026c56494dab01f","schema_version":"1.0","event_id":"sha256:98c8ff244fe048d44b271c61dae7c7d35d4b3fa061599e25a026c56494dab01f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FXVEAK6I4SB2RR32NBJ7IOJNUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The DoF of the K-user Interference Channel with a Cognitive Relay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anas Chaaban, Aydin Sezgin","submitted_at":"2012-07-02T10:49:34Z","abstract_excerpt":"It was shown recently that the 2-user interference channel with a cognitive relay (IC-CR) has full degrees of freedom (DoF) almost surely, that is, 2 DoF. The purpose of this work is to check whether the DoF of the $K$-user IC-CR, consisting of $K$ user pairs and a cognitive relay, follow as a straight forward extension of the 2-user case. As it turns out, this is not the case. The $K$-user IC-CR is shown to have $2K/3$ DoF if $K>2$ for the when the channel is time varying, achievable using interference alignment. Thus, while the basic $K$-user IC with time varying channel coefficients has 1/2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0337","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OkhYwZnGA43x2iBT8cLwkEKEFSjJjh1F9RjLOlVaH3SDSvjZC+Y6op6qhxLPdKu6iLERU/yOiDC3rOR1XRfrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:54:04.753403Z"},"content_sha256":"c45b23102b4f5b2d5382ba6e7a6653b369ce1519463f831cbe7687f7ea9559bd","schema_version":"1.0","event_id":"sha256:c45b23102b4f5b2d5382ba6e7a6653b369ce1519463f831cbe7687f7ea9559bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU/bundle.json","state_url":"https://pith.science/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T22:54:04Z","links":{"resolver":"https://pith.science/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU","bundle":"https://pith.science/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU/bundle.json","state":"https://pith.science/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXVEAK6I4SB2RR32NBJ7IOJNUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FXVEAK6I4SB2RR32NBJ7IOJNUU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e7dbfcb9167253a00f3513d0190a0074726811e2162cf39329542c7b3b545125","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T10:49:34Z","title_canon_sha256":"c7c62628d78aecea939a236364e91e8b607217fc711b108ff9c1d396aa085106"},"schema_version":"1.0","source":{"id":"1207.0337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0337","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0337v1","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0337","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"FXVEAK6I4SB2","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FXVEAK6I4SB2RR32","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FXVEAK6I","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:c45b23102b4f5b2d5382ba6e7a6653b369ce1519463f831cbe7687f7ea9559bd","target":"graph","created_at":"2026-05-18T03:51:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It was shown recently that the 2-user interference channel with a cognitive relay (IC-CR) has full degrees of freedom (DoF) almost surely, that is, 2 DoF. The purpose of this work is to check whether the DoF of the $K$-user IC-CR, consisting of $K$ user pairs and a cognitive relay, follow as a straight forward extension of the 2-user case. As it turns out, this is not the case. The $K$-user IC-CR is shown to have $2K/3$ DoF if $K>2$ for the when the channel is time varying, achievable using interference alignment. Thus, while the basic $K$-user IC with time varying channel coefficients has 1/2","authors_text":"Anas Chaaban, Aydin Sezgin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T10:49:34Z","title":"The DoF of the K-user Interference Channel with a Cognitive Relay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0337","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:98c8ff244fe048d44b271c61dae7c7d35d4b3fa061599e25a026c56494dab01f","target":"record","created_at":"2026-05-18T03:51:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e7dbfcb9167253a00f3513d0190a0074726811e2162cf39329542c7b3b545125","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T10:49:34Z","title_canon_sha256":"c7c62628d78aecea939a236364e91e8b607217fc711b108ff9c1d396aa085106"},"schema_version":"1.0","source":{"id":"1207.0337","kind":"arxiv","version":1}},"canonical_sha256":"2dea402bc8e483a8c77a6853f4392da508679e11ae40ae3ec3c894dc1b2063b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2dea402bc8e483a8c77a6853f4392da508679e11ae40ae3ec3c894dc1b2063b0","first_computed_at":"2026-05-18T03:51:59.581328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:59.581328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9ZL8RaZAxRjgECl+pUC9RwP2JuiF2/SWElG0RYGEdczwiFS+61QAykjbuF8ZCNQQ2MySxSyOuToPic8OpIcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:59.581844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98c8ff244fe048d44b271c61dae7c7d35d4b3fa061599e25a026c56494dab01f","sha256:c45b23102b4f5b2d5382ba6e7a6653b369ce1519463f831cbe7687f7ea9559bd"],"state_sha256":"f58d5e74b4421a349de13237e1547bf05107ea291dee0f8fbb3102af9c119630"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xecA1oqe9tmSCGMsI6XnioG+u/oXX/ukd/WfWjES8QPBtadlwASQ8loqk28CBq9yXYovYCP8hhRBhMdmUWiyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:54:04.756681Z","bundle_sha256":"973ce4a045b559651000073ca08649fc685ed2241767506fc6d2324d7fc07963"}}